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Some Applications of the Theory of Assemblages

Published online by Cambridge University Press:  03 November 2016

Arnold Emch
Arnold Emch*
Affiliation:
University of Colorado
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Extract

In order to be able to apply the theory of real numbers to measurable quantities, in particular to linear magnitudes, it is convenient to make use of the theory of groups (displacements). Thus, if B, C, D, …, Y are successive points on a continuous line between the extremities A and Z,

AB+BC+CD+…+YZ=AZ,

where AB, BC, … are arcs or consecutive displacements on the given line.

Type
Research Article
Information
The Mathematical Gazette , Volume 2 , Issue 33 , May 1902 , pp. 173 - 175
Copyright
Copyright © Mathematical Association 1902

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References

page 173 note * See in this connection,

Lagrange: Lectures on Elementary Mathematics, p. 3; translation by Th. J. Carnack.

Dedekind: Essays on the Theory of Numbers, pp. 1-27; translation by Prof. Beeman.

E. Borel, Leçons sur la Théorie des Fonctions, vol. i., p. 111.

page 173 note † Any other closed curve would do; the circle has been chosen on account of its simplicity.

page 174 note * See an interesting note of E. Maillet, Comptes Rendus, vol. cxxxiii., No. 20, pp. 782-784. “Sur les équations différentielles rationelles.”